What is A^-1 for matrix A?

Question 48

EasyOriginal question

What is $A^{-1}$ for $A = \begin{bmatrix}3 & 2 \\ 4 & 3\end{bmatrix}$ ?

\begin{bmatrix}3 & 4 \\ 2 & 3\end{bmatrix}

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\begin{bmatrix}-3 & 2 \\ 4 & -3\end{bmatrix}

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\begin{bmatrix}3 & -4 \\ -2 & 3\end{bmatrix}

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\begin{bmatrix}3 & -2 \\ -4 & 3\end{bmatrix}

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CorrectNot quiteAnswer D

Correct answer: D

$|A| = 9 - 8 = 1$ , which is not 0, so the inverse exists.
$A^{-1} = \frac{1}{|A|}\operatorname{adj} A = \begin{bmatrix}3 & -2 \\ -4 & 3\end{bmatrix}$ .

Worth noting

$\begin{bmatrix}3 & -4 \\ -2 & 3\end{bmatrix}$ is the cofactor matrix, not yet transposed into the adjoint.

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